Puzzle

ABSTRACT

A family of three-dimensional puzzles, each puzzle having six identical pieces. Each of the individual pieces in each puzzle includes a pair of members, each of which defines a prism of equilateral triangular cross-sectional shape. The prisms in each piece are arranged so that their longitudinal axes are skew to each other and so that one edge of one of the prisms intersects an edge of the other of the prisms at a specific angle. The six identical pieces in each puzzle can be assembled to an interlocking three-dimensional solution. While each of the puzzles in the family is formed from pieces having different shapes, the pieces from one of the puzzles can be interlocked with other pieces of other puzzles to form hybrid solutions.

United States Patent n 1 Coffin 1 1 May 27, 1975 i 1 PUZZLE [76] Inventor: Stewart '1. Coffm, Old Sudbury Rd.,

Lincoln, Mass. 01773 [22] Filed: May 18, 1973 [21] Appl. No.: 361,568

{52] 11.8. C1. 273/160 [51] Int. Cl. A631 9/12 [58] Field of Search 273/160; D34/5 M [56] References Cited UNITED STATES PATENTS 524,212 8/1894 Porter 273/160 766,444 8/1904 Hoy 273/160 779,121 1/1905 Ford 273/160 2,836,421 5/1958 Turner 273/160 FOREIGN PATENTS OR APPLlCATlONS 245.402 7/ 1947 Switzerland ..L 273/ 160 Primary Examiner-Anton O; Oechsle Attorney, Agent, or Firm-Arthur Z. Bookstein, Esq.

[57 1 ABSTRACT A family of three-dimensional puzzles, each puzzle having six identical pieces. Each of the individual pieces in each puzzle includes a pair of members, each of which defines a prism of equilateral triangular cross-sectional shape. The prisms in each piece are arranged so that their longitudinal axes are skew to each other and so that one edge of one of the prisms intersects an edge of the other of the prisms at a specific angle. The six identical pieces in each puzzle can be assembled to an interlocking three-dimensional solution. While each of the puzzles in the family is formed from pieces havir'zg different shapes, the pieces from one of the puzales can be interlocked with other pieces of other puzzles to form hybrid solutions.

5 Claims; 37 Drawing Figures SHEET w mgn am 2 71975 \qm 2E mm E w. H m n in HH PATENTEB RAY 27 m5 SHEET PATENTEB MAY 27 I975 SHEET BACKGROUND AND SUMMARY OF THE INVENTION This invention relates to puzzles and, more particu larly, three-dimensional. spacial relation puzzles. The basic puzzle includes six pieces. each of the pieces being formed from a pair of members having edges which define an equilateral triangular prism. In each piece of each puzzle the prismatic members are arranged so that their longitudinal axes are askew and with an edge of one of the prisms intersecting an edge of one of the other prism at an angle equal to approximately 109.5". The prism-defining members of each piece are secured together by an intermediate connecting structure which is the same for each of the six pieces in a particular puzzle. The intermediate members also are formed to include faces and/or surfaces which engage with like faces and/or surfaces on the other intermediate members of the pieces in a particular puzzle to assist in the interlocking placement of the pieces when assembling the puzzle. While each of the six pieces in a given puzzle is identical to the other pieces in that puzzle, the pieces of different puzzles vary in the manner in which the ends of the prismatic members are formed. The ends typically are cut off along planes which make a particular selected angle with the axis of the prism. Thus, while the puzzle pieces in each puzzle are assembled in a manner in which the prisms of each piece bear the same angular relationships to the prisms in the other puzzle pieces, the external appearance of the assembled puzzles vary widely. In addition, selected portions of the pieces in the puzzles can be hollowed-out which has the effect of increasing substantially the apparent complexity of the pieces. When the hollowed-out portions are exposed exteriorly of the assembled puzzle they provide additional distinctions between the appearance of the assembled puzzles.

The configuration of the puzzle pieces is such that puzzle pieces from one puzzle can be interchanged with pieces from other puzzles. Another feature of the family of puzzles is that puzzles can be interconnected to form larger puzzles of more than six pieces. One of the techniques to this end relates to the provision of a double piece," a portion of which can be interlocked with one of each of a pair of puzzles to join the separate puzzles together.

A further feature common to all of the puzzles described herein is that the six pieces in each puzzle can be assembled into two subassemblies of three pieces each, which subassemblies are of different geometrical configuration and in which the two subassemblies can be joined to each other to form the final solved assembly.

It is among the objects of my invention to provide a family of three-dimensional puzzles in which each piece of each puzzle is formed from a pair of members which define a prismatic shape of equilateral triangular cross-sectional configuration.

A further object of the invention is to provide a family of puzzles of the type described in which pieces from one puzzle may be interlocked with pieces of other puzzles of the family to form hybrid solutions as well as puzzles of more than six pieces.

DESCRIPTION OF THE DRAWINGS The foregoing objects and advantages of the invention will be understood more fully from the following detailed description thereof, with reference to the accompanying drawings wherein:

FIGS. la-lc illustrate the fundamental relationship between the prismatic members of each puzzle piece in each of the puzzles with FIG. la being a view as seen axially and from the end of one of the prismatic members in the puzzle piece, FIG. lb being an illustration similar to that of FIG. la but with the puzzle piece having been rotated about a vertical axis, and FIG. 1c being a plan view of the prismatic arrangement shown in FIG. 1b;

FIGS. 20-20 illustrate, in the same arrangement as FIGS. la-lc, the addition of an intermediate member by which the prismatic members are secured together;

FIGS. 3a-3c illustrate the arrangements shown in FIGS. 2a-2c but with portions of the prismatic members cut off, and FIG. 3d is an illustration of the form of puzzle piece shown in FIG. 30 as seen along the line Sci-3d,-

FIG. 4 is an illustration of the puzzle piece shown in FIGS. 3a3d but with selected portions of the piece hollowed-out;

FIG. 5 is an exploded illustration of a puzzle formed from six pieces of the type shown in FIG. 4;

FIG. 6 is an illustration of the puzzle pieces shown in FIG. 5 after they have been assembled into two subassemblies of three pieces each and in which the two subassemblies are of different configuration;

FIG. 7 is an illustration of the six puzzle pieces after the two subassemblies of FIG. 6 have been joined;

FIG. 7a is an illustration of the appearance of the completed puzzle shown in FIG. 7 as made from the hollowed-out pieces shown in FIG. 4;

FIG. 8 is a view of the upper of the subassemblies shown in FIG. 6 as seen along the axis of symmetry of the subassembly;

FIG. 9 is an illustration of the lower subassembly of FIG. 6 as seen along its axis of symmetry;

FIG. 10 is an illustration similar to FIG. 9 with the puzzle pieces tilted slightly radially and outwardly to expose the mating surfaces of the oblate octahedral im mediate members;

FIG. 11 is an illustration of another type of puzzle piece;

FIG. 12 is an illustration of the puzzle made from six of the pieces shown in FIG. 11 when fully assembled;

FIG. 13 is an illustration of still another type of puzzle piece;

FIG. 14 is an illustration of a puzzle assembled from six pieces of the type shown in FIG. 13;

FIGS. 15, 16 and 17 are illustrations of still another type of puzzle piece as seen in the same manner as FIGS. 30, 3b and 3c were presented;

FIG. 18 is an illustration of a puzzle assembled from six pieces of the type shown in FIGS. 15-17;

FIG. 19 is an illustration of the manner in which a six piece puzzle may be assembled from three differently shaped pairs of puzzle pieces with the upper subassembly being exploded and the lower subassembly shown in its assembled configuration;

FIG. 20 is an illustration of the completed puzzle of FIG. 19;

FIG. 21 is a perspective illustration of a double puzzle piece;

FIG. 22 is a plan view of FIG. 21'.

FIG. 23 is an illustration of the double puzzle piece as seen along the line 2323 of FIG. 22;

FIG. 24 is an illustration of the double puzzle piece as seen along the line 2424 of FIG. 23;

FIG. 25 is an exploded view of three double puzzle pieces showing the manner in which they may be joined to form a subassembly;

FIG. 26 is an illustration of a completely assembled puzzle formed from six double pieces as seen along the axis of symmetry of one of said pieces.

FIGS. 27. 28 and 29 show the manner in which a multiple puzzle assembly may be built by utilizing the double puzzle piece shown in FIG. 21.

DESCRIPTION OF THE PREFERRED EMBODIMENT FIGS. ll all relate to one of the puzzles in the family, shown in assembled form in FIG. 7 and in which an individual puzzle piece of that puzzle is shown in FIG. 3. FIG. 4 shows what is substantially the same puzzle piece shown in FIG. 3 except that it has been hollowedout which. while functioning in the same manner as the piece shown in FIG. 3, presents a more complex appearance of the puzzle piece as well as the finally assembled puzzle. For ease of explanation of the complex shape of the puzzle piece FIGS. 13 show, progressively. how the puzzle piece may be considered as being formed from a pair of equilateral prismatic members and their relationship to the intermediate connecting member as described above.

FIGS. lal(' show a pair of prisms P. P of equilateral triangular cross-sectional shape with their longitudinal axes A. A askew to each other. The prismatic mem bers in each puzzle piece are arranged so that an edge of one intersects an edge 10 of the other at an intersection point 12. The intersecting inner edges define an angle 9 of 109.5". The prismatic members P, P also are arranged so that their faces 14, 14 opposite their respective intersecting edges 10, 10' lie substantially parallel to each other and to the plane defined by the intersecting inner edges l0, 10'. This prismatic relationship is found in each piece of each puzzle of the invention.

In order to secure the prismatic members of each puzzle piece together and to permit final assembly of the pieces in each puzzle. each of the puzzle pieces includes an intermediate connecting member 16. FIGS. 2a-2r show the appearance of the prismatic members of FIGS. Iu-lc with the addition of the intermediate connecting member 16. In the embodiment shown in FIGS. 2c the intermediate member 16 is in the form of an oblate octahedron. One side of the octahedron is fully exposed between the angle 9 defined by the prisms P. P at their intersections and the other side of the octahedron has a pair of opposite faces which join and lie in a common plane with one face of each of the pris matic members. In the drawings, those surfaces of the prisms and intermediate member which face inwardly from the angle 9 (those surfaces which may be seen in any of FIGS. lb. 2b or 3b) will be referred to as in wardly or forwardly facing surfaces. Thus, the surfaces of the oblate octahedron indicated at F1, F2, F3 and F4 as well as the surfaces l8, 18' of the prisms P. P' will be referred to as inwardly or forwardly facing surfaces.

the double piece shown in Conversely. those surfaces which face outwardly such as the prism surfaces 20, 20 will be referred to as outwardly facing. It should be noted in this regard that the outwardly facing octahedral surfaces which join and lie in common with either of the forwardly facing surfaces I8 or I8 of the prisms P, P are not exposed but may nevertheless be considered as existing. Thus. the rearwardly facing surfaces of the oblate octahedron 16 may be referred to as surfaces RI, R2, R3 and R4 in the same sense as faces Fl-F4 of the forwardly facing octahedral surfaces were designated. In accordance with the foregoing surface designations, it will be seen that surface R1 of the octahedron l6 lies against and interfaces with the inner or rearward facing surface 18 of prism P and the rearwardly facing surface R3 of the octahedron l6 lies against forwardly facing surface 18' of the prism P. It may be noted further that the rearward apex of the oblate octahedron I6 coincides with the intersection point 12.

FIGS. 30, b and c show the arrangements of 2ac except that end portions of the prismatic members have been severed along oblique planes which. typically. may make an angle of 5444. From FIG. 30 it may be seen that the left end of the prism P has been severed along a plane 22 which. for this particular puzzle. is parallel to the inwardly facing surface 18' of the other prismatic member P. The same is true of the corrc sponding end of the other prismatic member P' which is similarly obliquely severed along a plane 22 which bears the same relationship to the corresponding surface I8 of the prismatic member P (FIG. 3b). Additionally. the ends of the prismatic members which are more adjacent the intermediate members 16 are severed along planes which define extensions of the planes of rearward faces of the oblate octahedral intermediate member 16. Thus. it may be seen from FIG. 3c that the prism P has been severed along a plane which is an extension of the plane in which the face R2 of the intermediate member 16 and also the rearward face 20' of the other prismatic member 10' lie. The other prismatic member P similarly is cut off at its corresponding end and the resulting shape of the puzzle piece is that shown in FIG. 3a-3d. It may be noted that the intersecting point I2 still remains definable as suggested in FIG. 3c. The resulting puzzle piece has an axis of symmetry which extends along a line which joins the intersection point 12 and the forward apex of the octahedron 24.

FIG. 4 shows what is geometrically the same piece shown in FIG. 3a3d except that portions of the piece have been hollowed-out. The effect of the selective hollowing-out of the piece serves a number of purposes, such as to make the piece visually more complicated as well as to save material in the molding of the piece and to facilitate molding of the piece in accordance with conventional known plastic molding techniques. The apparent increased visual complexity of the arrangement by reason of the hoIlowing-out of each of the puzzle pieces can be seen from a comparison of FIGS. 7 and 7a. FIG. 7 shows the fully assembled puzzle made from solid pieces. as those in FIG. 3a3d. and FIG. 7a shows the finally assembled appearance of the same puzzle made from the hollowedout pieces shown in FIG. 4.

FIGS. S7 show the sequential manner in which the six identical puzzle pieces of FIGS. 3a-3d may be assembled. The manner of assembly is to separate the six pieces into two subgroups of three pieces each, then to assemble the subgroups into two subassemblies (FIG. 6) and then to mate the two subassemblies to the final full puzzle (FIG. 7). It should be noted that in each of the puzzles the two subgroups of three pieces each can be assembled in two geometrically different arrangements (see FIG. 6).

To assemble the puzzle having six pieces shaped as shown in FIGS. 3a3d, the six pieces are separated into two groups of three pieces each. Each of the groups is assembled, in the manner described below, into the two geometrically different subassemblies shown in FIG. 6. To form the upper of the subassemblies shown in FIG. 6, the three pieces indicated at A, B, and C (FIG. 5) are manipulated to bring together certain of the inwardly facing octahedral surfaces Fl-F4 in a manner in which the inner octahedral apex 24 of each of the pieces A, B and C meet at a common point. As shown in FIG. 6, this may be accomplished by orienting the prisms P of each pieces A, B and C so that their axes are parallel, then bringing together the octahedral face F3 of piece A with octahedral face F2 of piece B, then bringing together in like manner octahedral face F2 of piece C with face F3 of piece B and then face F3 of piece C with face F2 of piece A. In this subassembly the prismatic members P of pieces A, B and C are in parallel when assembled. FIG. 8 shows still another view of the upper subassembly as seen along the axis of symmetry from the free ends of the prisms P.

The lower of the subassemblies shown in FIG. 6 may be assembled in like fashion but by mating different of the inwardly facing octahedral faces of the puzzle pieces D, E and F. As shown in FIGS. 5 and 10 face F3 of puzzle piece D mates with face F4 of piece E, face F3 of piece E mates with face F4 of piece F and face F3 of piece F mates with face F4 of piece D. When this subassembly is formed it has an appearance, in plan, as shown in FIG. 9. FIG. 10 is a view similar to FIG. 9 except that the puzzle pieces D, E and F are tilted slightly outwardly and away from the axis of symmetry to expose the faces F3, F4 of the pieces and to illustrate more fully how those faces engage each other. It will be seen from FIG. 9 that three 60 openings 30 are defined (when viewed along the axis of symmetry) and are receptive to the three parallel prisms P in the other subassembly. The surfaces which define the openings 30 can be seen from the lower subassembly in FIGS. 6. The angle 30 is defined by the surface 18 of puzzle piece D and surface R2 of puzzle piece F. The subassemblies then are brought together as shown in FIGS. 6 and 7 with the prisms P and V notches 30 mating to form fully the assembled puzzle shown in FIG. 7.

It may be noted that in each of the subassemblies, the symmetrical axes of each of the pieces are disposed in mutually perpendicular relationship. This characteristic is found in each of the puzzles described herein.

FIG. 11 shows an illustrative individual puzzle piece from another puzzle in the family of puzzles, which piece embodies the same principles as previously described. This puzzle piece includes the equilateral triangular prismatic members P, P and the oblate octahedral intermediate member 16. The oblique planes along which the prismatic members P, P are cut off from the configuration shown in FIGS. 2a-2c is different which gives the puzzle piece in FIG. 11 a quite different appearance. The puzzle piece shown in FIG. 11 is formed from that shown in FIGS. 2a-2c by severing the prism P at one end along a plane which is an extension of the plane defined by face F4 of the octahedral member and by severing the other end of the prismatic member P along a plane which bisects the angle defined by the planes of the octahedral faces F2 and F3, which passes diagonally through the octahedral member, the intersection point 12 and the octahedral apex 24. Similarly, the prism P is severed along, at one end, a corresponding and, at the other end is severed along a plane which is an extension of the plane defined by face F2 of the octahedral member. The assembly of six puzzle pieces of this configuration is achieved in the same manner as that previously described except that the geometrical configurations of the subassemblies differ from those shown in FIG. 6. FIG. 12 shows the appearance of a completely assembled puzzle using six pieces of the type shown in FIG. 11. It will be appreciated that the puzzle piece shown in FIG. 11 may be similarly hollowed-out, which makes the visual appearance of the individual pieces as well as the finally assembled puzzle more complex.

FIG. 13 shows still another puzzle piece which is substantially the same as that shown in FIG. 11 except that it includes an additional pair of prismatic members P" and P'. The relationship between prismatic members P" and P is the same as that between the prismatic members P, P' except that it is reversed with respect to the faces of the octahedral member l6. The assembly technique for a six piece puzzle including the type of puzzle piece shown in FIG. 13 is the same as described previously and FIG. 14 shows such a puzzle fully assem bled.

A further feature of the invention is that, while the puzzle pieces shown in the three previously described embodiments have substantially different appearances both individually and in their finally assembled individual forms, they can, nevertheless, be intermingled to form a six-piece puzzle from more than one kind of piece. They can also be assembled to form a large hy' brid puzzle of substantially more than six pieces.

FIGS. 19 and 20 show a six-piece puzzle formed from three differently shaped pieces, there being two identical pieces of each in the puzzle. FIG. 19, which is a partially exploded illustration of this puzzle, similar to that in FIG. 5, shows an upper, exploded subassembly and a lower, assembled subassembly. Each of the upper and lower subassemblies are formed from one each of the pieces shown in FIGS. 3, 11 and I3 and are designated by reference characters, 3, ll, 13 which correspond to said figures. The technique of assembly is the same as previously described. Each of the subassemblies are made by bringing the selected faces of the octahedral member in abutment with each other and in a manner in which the axes of symmetry of the assembled pieces are mutually perpendicular to each other. FIG. 20 is an illustration of the fully assembled puzzle of FIG. 19. It may be noted that in order to effect the interchangeability of the pieces, they should be made to the same scale.

FIGS. 21 24 show still another type of puzzle piece, referred to herein as a double piece, with which six such pieces may be assembled into the puzzle shown in FIG. 26. This type of puzzle piece, however, also may be employed as a common piece to two puzzles to enable the two puzzles to be interlocked together as sug gested in FIGS. 27-29 (described below). This piece, indicated generally at 50, may be considered as being formed from a pair of previously described puzzle pieces which are joined together at a common intersec tion point 12' with the apices of the octahedral connecting member extending away from each other and in which the axes of symmetry of the joined pieces are coincident. Thus, as shown in FIG. 21, the double piece 50 includes a pair of octahedral connecting members 52, 52' which have apices 24, 24' respectively. The octahedral member 52 may be considered as being associated with prismatic members lying along the axes Z, Z. The four prismatic members in the double piece 50 are severed along oblique planes to the shape shown in FIGS. 21-24 from which it may be seen that a pair of right angle V-notches 54 are presented as seen best in FIG. 23. In order to reinforce this double puzzle piece, a pair of integral ribs 56 preferably are formed halfway along the apex of the V-grooves 54 as shown. FIG. 25 shows the manner in which three such double pieces may be assembled in a subassembly which may subsequently be joined to a similar subassembly made from three other double pieces. The technique of assembly is the same of that described with the previous embodiment in which the octahedral intermediate members 52 of three pieces are brought together in a manner in which their axes of symmetry are mutually perpendicular. FIG. 26 shows a final assembly of six such pieces as seen along one of the three Cartesian axes of symmetry.

FIGS. 27, 28 and 29 show the manner in which the double piece of FIG. 21 may be employed to form a multiple puzzle assembly. While the double piece may be used in conjunction with any of the puzzle configurations described above, it is illustrated as being used with the puzzle shown in FIGS. -7. The manner of assembly of the multiple puzzle assembly using the double piece is substantially the same as that described before except that one of the subassemblies includes, as a substituted piece, the double piece 50. This subassembly has the appearance shown in perspective in FIG. 28. FIG. 27 shows, in a plan view similar to FIG. 8, the appearance of the subassembly. With one of the puzzles being assembled using the double piece 50 and having the appearance shown in FIG. 28, it will be seen that one of the octahedral members of the double piece 50 is exposed. This exposed portion of the double piece 50 is incorporated as an element in another puzzle and thus effectively joins two puzzles together as shown in FIG. 29. It may be noted that while FIG. 29 shows the double piece 50 linking two identical puzzles, the linked puzzles need not be identical but may be builtup from any arrangement of puzzle pieces as previously described.

FIGS. -17 show, in the same sequential presentation, a FIGS. 30-30 still another type of puzzle piece which forms part of the invention. As in the previous embodiments, the fundamental characteristics of the puzzle piece include a pair of equilateral triangular prismatic members P, P (here hollowed-out to general V-shaped cross-section) which are arranged in skew and intersecting at edges 10, 10 at an intersection point 12 which defines an angle of approximately l09.5. The outer prism surfaces 14, 14' are substantially parallel to each other. The prisms are secured together by an intermediate member 40 which, in this embodiment, does not take the form of the oblate octa hedron previously described but, instead, is in the form of a flat member which extends generally along the plane defined by the intersecting edges 10, 10' of the prismatic members, The intermediate member 40 is substantially in the shape of a parallelogram and has beveled edges 42, 42' which each make an angle of with the intersection plane. The puzzle formed from six of these pieces also is assembled by forming two subassemblies of different geometrical configurations of three pieces each and then mating those subassemblies. With this puzzle, however, the beveled edges 40, 42 of the intermediate members 40 engage corresponding beveled members of other of the pieces in the puzzle. The subassemblies formed with these pieces are somewhat similar to those shown in FIG. 6 in that one of the subassemblies includes three prismatic members P or P oriented with their axes substantially parallel to each other and the other subassembly defines three triangular openings into which the prismatic members of the first subassembly may be inserted. The finally assembled puzzle has an appearance such as that shown in FIG. 18.

It should be noted that the puzzle piece shown in FIGS. l5-l7 differs somewhat from the puzzle pieces previously described in that the rearwardly extending ldS of the prismatic members extend rearwardly beyond the intersection point (see FIG. 15), This enables a puzzle to be assembled with at least one of the pieces being inverted in the final assembly. This manner of assembly results in an arrangement somewhat similar to that shown in FIG. 18 except that the more forward ends of the prismatic members protrude outwardly of the main body of the puzzle in somewhat rabbit-ear.

The individual pieces of any given puzzle may be made from plastic or other appropriate materials. Added interest and complexity of the puzzles may be achieved by making them of various colors. Alternatively, they may be made from transparent plastic which enables the intersection of planes, lines, etc., at the interior of the assembled puzzles to be viewed.

It should be understood that the foregoing description of the invention is intended merely to be illustrative thereof and that other modifications and embodiments may be apparent to those skilled in the art without departing from its spirit.

Having thus described the invention what] desire to claim and secure by Letters Patent is:

l. A family of at least two three-dimensional puzzles, each puzzle having six identical pieces, each piece comprising:

a pair of members, each member defining a prismatic shape of equilateral triangular cross-section;

said members being arranged so that their longitudinal axes are askew, and with a longitudinal edge line of one of said prismatic members substantially intersecting a longitudinal edge line of the other of said prismatic members at an angle of approximately l09.5;

said prismatic members being oriented so that their surfaces which are opposite their intersecting edges are substantially parallel to each other;

an intermediate member connecting said prismatic members to secure said prismatic members together, said intermediate member having selected surfaces which are engageable with corresponding surfaces of intermediate members of the other pieces of said puzzle to facilitate orientation and mating of said puzzle pieces with each outer;

each intermediate member of each piece of each of said puzzles being substantially identical in shape and each piece of each of said puzzles being of the same dimensional scale, the pieces from each of said puzzles being interchangeable with the pieces of the other of said puzzles;

the ends of each of the prismatic members in the pieces of a particular puzzle being cut off along the planes defining an oblique angle with the axis of said prismatic member; and

the ends of the prismatic members in the puzzle pieces of one of said puzzles being cut off along oblique planes which are different from the oblique planes along which the ends of the prismatic members of other pieces of the other puzzles in said family are cut off.

2. A family of at least two three-dimensional puzzles,

each puzzle having six pieces, each piece comprising:

a pair of members, each member defining a prismatic shape of equilateral triangular cross-section;

said members being arranged so that their longitudinal axes are askew, and with a longitudinal edge line of one of said prismatic members substantially intersecting a longitudinal edge line of the other of said prismatic members at an angle of approximately l09.5;

said prismatic members being oriented so that their surfaces which are opposite their intersecting edges are substantially parallel to each other;

an intermediate member connecting said prismatic members to secure said prismatic members together, said intermediate member having selected surfaces which are engageable with corresponding surfaces of intermediate members of the other pieces of said puzzle to facilitate orientation and mating of said puzzle pieces with each other;

each intermediate member of each piece of each of said puzzles being substantially identical in shape and each piece of each of said puzzles being of the same dimensional scale, the pieces from each of said puzzles being interchangeable with the pieces of the other of said puzzles;

said intermediate member comprising means integral with said prismatic members and defining an oblate octahedron in which one apex of the octahedron coincides with said intersection point; and

an additional double piece formed from a pair of integral puzzles pieces having a common intersection point and having oblate octahedral intermediate members lying along a common axis of symmetry which intersects the intersection point of each of said joined puzzle pieces, the prismatic members of each of said joined members in said double piece 5 being severed along oblique planes which define, on each side of said axis of symmetry, a V-shaped groove which intersects the common points of intersection of the joined pieces, said double piece being constructed and arranged to interlock with a pair of puzzles in said family thereof. 3. A family of puzzles as defined in claim 2 further comprising:

an additional puzzle having six pieces, each of said pieces comprising one of said double pieces. 4. A three-dimensional puzzle having six pieces, each piece comprising:

a pair of members, each member defining a prismatic shape of equilateral cross-section; said members being arranged so that their longitudinal axes are askew, and with a longitudinal edge line of one of said prismatic members substantially intersecting a longitudinal edge line of the other of said prismatic members at an angle of approximately 109.5"; said prismatic members being oriented so that surfaces which are opposite their intersecting edges are substantially parallel to each other; an intermediate member connecting said prismatic members to secure said prismatic members together and to facilitate orientation and mating of said puzzle pieces with each other, said intermediate member being of generally planar, substantially parallelogram configuration and lying substantially in a plane which coincides with the plane defined by the intersecting edges of said prismatic member, said intermediate member having forwardly facing edges which lie in a plane which make an angle of approximately 60 with said plane defined by said intersecting edges of said prismatic members, the forwardmost portion of said intermediate member defining a point which, in cooperation with the intersection point, defines an axis of symmetry of the puzzle piece. 5. A puzzle as defined in claim 4 wherein each of said puzzle pieces further comprises:

each of said prismatic members extending rearwardly beyond the point of intersection of said edgesv i 

1. A family of at least two three-dimensional puzzles, each puzzle having six identical pieces, each piece comprising: a pair of members, each member defining a prismatic shape of equilateral triangular cross-section; said members being arranged so that their longitudinal axes are askew, and with a longitudinal edge line of one of said prismatic members substantially intersecting a longitudinal edge line of the other of said prismatic members at an angle of approximately 109.5*; said prismatic members being oriented so that their surfaces which are opposite their intersecting edges are substantially parallel to each other; an intermediate member connecting said prismatic members to secure said prismatic members together, said intermediate member having selected surfaces which are engageable with corresponding surfaces of intermediate members of the other pieces of said puzzle to facilitate orientation and mating of said puzzle pieces with each other; each intermediate member of each piece of each of said puzzles being substantially identical in shape and each piece of each of said puzzles being of the same dimensional scale, the pieces from each of said puzzles being interchangeable with the pieces of the other of said puzzles; the ends of each of the prismatic members in the pieces of a particular puzzle being cut off along the planes defining an oblique angle with the axis of said prismatic member; and the ends of the prismatic members in the puzzle pieces of one of said puzzles being cut off along oblique planes which are different from the oblique planes along which the ends of the prismatic members of other pieces of the other puzzles in said family are cut off.
 2. A family of at least two three-dimensional puzzles, each puzzle having six pieces, each piece comprising: a pair of members, each member defining a prismatic shape of equilateral triangular cross-section; said members being arranged so that their longitudinal axes are askew, and with a longitudinal edge line of one of said prismatic members substantially intersecting a longitudinal edge line of the other of said prismatic members at an angle of approximately 109.5*; said prismatic members being oriented so that their surfaces which are opposite their intersecting edges are substantially parallel to each other; an intermediate member connecting said prismatic members to secure said prismatic members together, said intermediate member having selected surfaces which are engageable with corresponding surfaces of intermediate members of the other pieces of said puzzle to facilitate orientation and mating of said puzzle pieces with each other; each intermediate member of each piece of each of said puzzles being substantially identical in shape and each piece of each of said puzzles being of the same dimensional scale, the pieces from each of said puzzles being interchangeable with the pieces of the other of said puzzles; said intermediate member comprising means integral with said prismatic members and defining an oblate octahedron in which one apex of the octahedron coincides with said intersection point; and an additional double piece formed from a pair of integral puzzles pieces having a common intersection point and having oblate octahedral intermediate members lying along a common axis of symmetry which intersects the intersection point of each of said joined puzzle pieces, the prismatic members of each of said joined members in said double piece being severed along oblique planes which define, on each side of said axis of symmetry, a V-shaped groove which intersects the common points of intersection of the joined pieces, said double piece being constructed and arranged to interlock with a pair of puzzles in said family thereof.
 3. A family of puzzles as defined in claim 2 further comprising: aN additional puzzle having six pieces, each of said pieces comprising one of said double pieces.
 4. A three-dimensional puzzle having six pieces, each piece comprising: a pair of members, each member defining a prismatic shape of equilateral cross-section; said members being arranged so that their longitudinal axes are askew, and with a longitudinal edge line of one of said prismatic members substantially intersecting a longitudinal edge line of the other of said prismatic members at an angle of approximately 109.5*; said prismatic members being oriented so that surfaces which are opposite their intersecting edges are substantially parallel to each other; an intermediate member connecting said prismatic members to secure said prismatic members together and to facilitate orientation and mating of said puzzle pieces with each other, said intermediate member being of generally planar, substantially parallelogram configuration and lying substantially in a plane which coincides with the plane defined by the intersecting edges of said prismatic member, said intermediate member having forwardly facing edges which lie in a plane which make an angle of approximately 60* with said plane defined by said intersecting edges of said prismatic members, the forwardmost portion of said intermediate member defining a point which, in cooperation with the intersection point, defines an axis of symmetry of the puzzle piece.
 5. A puzzle as defined in claim 4 wherein each of said puzzle pieces further comprises: each of said prismatic members extending rearwardly beyond the point of intersection of said edges. 